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Hopf bifurcation control of the M–L neuron model with type I

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Abstract

Many neurological diseases are known to be caused by bifurcations induced by a change in the values of one or more regulating parameter of nervous systems. The bifurcation control may have potential applications in the diagnosis and therapy of these dynamical diseases. In this paper, a washout filter-aided dynamic feedback controller composed of the linear term and the nonlinear cubic term is employed to control the onset of Hopf bifurcation in the Morris–Lecar (M–L) neuron model with type I. It is shown that the linear term determines the location of the Hopf bifurcation, while the nonlinear cubic term regulates the criticality of the Hopf bifurcation, preventing it from occurring in a certain range of the externally applied current. The relationships among the externally applied current, the linear control gain and the reciprocal of the filter time constant are further systematically analyzed, which help to make the best choice from the feasible parameter space to achieve our control task. Simulation results are provided to illustrate the effectiveness of the proposed methods.

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Acknowledgments

The work is supported by the National Key Research and Development Program of China under Grant 2016YFB0800401, the National Natural Science Foundation of China under Grants 61621003, 61532020, 11472290, 61472027, 11475022, 11547006, 61503046, the Key Program of Frontier Science of the Chinese Academy of Sciences under Grant QYZDJ-SSW-JSC003, and Guangxi Education Department Key Laboratory of Symbolic Computation and Engineering Data Processing (No. FH201502).

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Authors and Affiliations

  1. School of Information and Mathematics, Yangtze University, Jingzhou, 434023, People’s Republic of China

    Chunli Huang & Wen Sun

  2. College of Information Science and Engineering, Huaqiao University, Xiamen, 361021, People’s Republic of China

    Zhigang Zheng

  3. Academy of Mathematics and Systems Science, CAS, Beijing, 100190, People’s Republic of China

    Jinhu Lu

  4. The Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia

    Jinhu Lu

  5. College of Mathematics and Statistics, Wuhan University, Wuhan, 430072, People’s Republic of China

    Shihua Chen

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  1. Chunli Huang
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  2. Wen Sun
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  3. Zhigang Zheng
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  4. Jinhu Lu
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Correspondence to Wen Sun.

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Huang, C., Sun, W., Zheng, Z. et al. Hopf bifurcation control of the M–L neuron model with type I. Nonlinear Dyn 87, 755–766 (2017). https://doi.org/10.1007/s11071-016-3073-x

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